From Example Problems
Jump to: navigation, search

Find the derivative of f(x)\, with respect to x\,: f(x)={\frac  {x\sin x}{e^{x}}}\,

This problem involves the quotient rule. But, on top of that, when taking the derivative of the top, you'll have to do a product rule.

f'(x)\, ={\frac  {e^{x}(x\cos x+\sin x)-xe^{x}\sin x}{(e^{x})^{2}}}\,
={\frac  {e^{x}(x\cos x-x\sin x+\sin x)}{(e^{x})^{2}}}\,
={\frac  {x\cos x-x\sin x+\sin x}{e^{x}}}\,

Main Page : Calculus